Sustainability and Rates of Change
Christopher L. Coughenour, Ph.D.
The Evergreen State College
July 27, 2011
Exercise: Global Crude Oil Production Rates
Global discoveries of oil reserves peaked in the early-mid 1960's (Longwell, 2002) and it is forecast by a number of observers that conventional oil production rates have peaked or will soon peak and begin to decline by approximately 2 billion barrels per day per year (Bentley, 2002). This remains a contentious issue, and certainly one with significant economic, political, and environmental consequences. At the heart of the issue is the claim that, by analyzing historical records of crude oil production rates, one can model and then make predictions about future crude oil production. Historically, nearly all oil produced has been from conventional sources using stable, conventional technology. Even if we can model and make predictive statements about conventional oil, what can we say about total petroleum production as biofuels, non-conventional sources, and increased recovery technology will likely become more prevalent? Let us first analyze the data on conventional oil production and then discuss how it may be interpreted in different ways.
1. Download the EIA data for global crude oil production since 1960. Also download the data from Campbell and Laherrere from 1930 to 1959.
2. Import the values into a new spreadsheet.
a. Organize the data into daily production rate (Q/t) in millions of barrels per day (mbd).
b. Calculate the annual production rate (Q/t) in billions of barrels per year (bby).
3a. Calculate cumulative oil production for the world in billions of barrels of oil (bbo) (oil produced before 1930 is taken as neglible relative to 20th and early 21st century production). This is the amount extracted (Q) up to 2009.
b. Plot global cumulative oil production.
c. Describe in words the behavior of the plotted data. How did oil production change with time?
d. Based on your observations, what may be a plausible model for oil production?
e. Write the equation for this model in terms of oil production, denoting the meanings of each of the variables and constants.
4. We will now try to fit this model to the oil data. To do so, we need to determine the values of the constants. One method of determining appropriate values for constants in this sort of model is to alter the model equation into an equation of a line. The model constants can then be computed from the constants in y = mx + b, nameley th slope and intercept.
a. Divide the model equation by Q and demonstrate that the new equation is that of a line.
b. What do y, m, x, and b represent in terms of oil production variables and constants? Hint: In both equations, Q is the independent variable.
c. Plot the data in this new form ([Q/t]/Q vs Q).
Observe that all of the data taken together do not form a line. Following the method of Deffeyes (2006) we will analyze the nearly linear trend line that occurs since 1983. This method was chosen because it is a straightforward way of calculating oil production constants without resorting to equivalent, but more complex methods employed by M. King Hubbert in his first predictions of oil production rates. Before 1983, the cumulative amount of oil produced was small and as the denominator Q tends toward zero, the y-axis values of production rate/Q become quite large.
d. Calculate the regression line for data since 1983.
e. What are the values of the oil production constants? Given these data only, given an estimate of the remaining accessible (conventional) oil in the world as of 2009.
f. Produce modelled cumulative oil production values (Q) from the year 1983 (t=0) using these oil production constants.
g. Re-plot cumulative oil production since 1930 and on the same graph include the modelled production since 1983. Does the model appear to be a good fit?
h. Now produce modelled cumulative oil production values (Q) since the year 1930 (t=-53). Plot these with the actual data since 1930. Note your observations.
i. Does it appear from the these graphs that production rates have reached a maximum?
j. Using "derivatives" on the modelled data, produce a curve for production rates from 1930 to 2009. Plot these modelled production rates with actual production rates for comparison.
k. Find the year of peak production in the world from the modelled data and from the actual data.
5. Given these data and analyses, what interpretations could one make about the modelling and its relation to past data? What about using the model to predict future oil production rates in the world? USGS (2000) estimates total recoverable oil in the world at over 3 trillion barrels. How may this affect predictions? For instance, the EIA predicts on the basis of these numbers and their own model that worldwide oil production will not peak until about 2044 (see Caruso, 2005).
What considerations should probably be made? What are potential factors that could cause future oil production to differ from predicted rates?